Did you try and calculate them via the field calculator?
Right-click the column heading and click "Field Calculator..." and in the box write "0" (without the quotation marks).
I did. The field calculator is grayed when I try.
The data were joined and the null values are non-matching records.
If IsNull([JoinedObjectIDField]) Then Output = "SomeValueWhenRecordsAreUnmatched" Else Output = [OriginalValueInOutputField] End If